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Iv) It should be stressed that no thermal equilibrium can ever be reached within a box with reflecting walls. The single monochromatic components of the electromagnetic field do not interact with each other, and hence no process can lead to thermal equilibrium in such a case. Fortunately, there are no perfect reflectors. (v) As far as the emission of radiation is concerned, all energy-balance arguments should take into account both induced emission and spontaneous emission. The former results from the interaction with an external field, whereas the latter may be due to energy acquired during previous collisions, or to previous interactions with an electromagnetic field.

For any closed curve C in the region R identified as the level set of a maximal family of pairwise commuting first integrals (the commutation property being valid with respect to Poisson brackets), the desired invariance principle can be stated in the form N pj dqj = nh. 4) C j=1 The level sets occurring here are either tori2 or cylinders. For multiperiodic evolution they are tori. If the integration is performed in a system of coordinates where the separation of variables is obtained, N N Kj pj dqj = j=1 Kj nj h.

E. 5) of arbitrary pairs of elements of F. 6) which provides a precise statement of the Ritz combination principle: the spectrum is endowed with a composition law, according to which the sum of the frequencies νi, j and νl,k is again a frequency of the spectrum only when l = j. Their combination is then expressed by Eq. 6). (e) From the knowledge of the absorption spectrum the energies En can be derived, because, once the constant h is known, the absorption spectrum makes it possible to determine E2 − E1 , E3 − E1 , .